Most of the factoring source code here was written by Ami Fischman and myself. We started futzing
around in 1995 while giving a seminar on eliptic curves. The code here is
not at all optimized - it is here for illustrative purposes, for you to
LEARN. We'd still like to shake out some bugs, so please mail us with code, suggestions for
improvement, or pointers to other places for info if ya got 'em.

The code below uses type Integer for its int type. I
suggest you use the gmp library with the Integer class that I wrote (see below), but you can use any class you wish.

Basic.cc
Factors integers using the "try every number before sqrt(n)" algorhithm.
Not very efficient at all. The better factoring programs use this method to
clear out all the small factors first, and then use a more powerful method,
like Pollard's 'P-1'...
Requires an Integer Class for the GMP
library

Fermat.cc
Fermat's algorithm is pretty good when the number you wish to factor has
two factors very near to sqrt(n). Otherwise, it is just as slow as the
basic division algorithm.
Requires an Integer Class for the GMP
library

Shor.cc
A simple algorithm based on looking at the size of certain Groups mod n.
It's only justification for existence is that it (theoreticaly) runs great
on quantum computers . . . but stinks on "normal computers". Only here
for illustrative purposes.
Requires an Integer Class for the GMP
library

Shanks.cc
Shank's square form method. I don't know much about this one. It's OK.
Requires an Integer Class for the GMP
library

Williams_p1.cc
William's 'P+1' method. I don't know much about this one either, but it
isn't too bad.
Requires an Integer Class for the GMP
library

Pollard_p1.cc Called
"Pollard's 'P-1' method" and is based upon Fermat's Little Theorem.
Not a bad little algorithm.
Requires an Integer Class for the GMP
library

Pollard_rho.cc Called "The
Pollard rho algorithm" and is also based upon Fermat's Little Theorem.
Faster than P-1. Very nice for general use (small numbers).
Requires an Integer Class for the GMP
library

Lenstra.cc
Factors integers based on H.W. Lenstra's algorhithm using eliptic curves.
This method hit the big time in the early 90's, but other more
sophisticated routines have since then eclipsed this fella.
Requires an Integer Class for the GMP
library

Dixon.cc
A "modular arithmetic" extension of Fermat's idea. Not to swift, but the
idea is fundamental if you wish to understand how the MPQS and NFS
algorithms work. This example here is not quite finished.
Requires an Integer Class for the GMP
library

A lot of this, and other algorithms, can also be found (all tar'ed up &
g-zipped) at Ami's program page.

gmp-2.0.2.tar.gz
Inorder to factor very large integers, you need a library to give you big
integers. This C library allows you to play with arbitrarily large
integers, and is supported by the GNU
project. When downloading, you should get this library from a GNU mirror site near
you.

Integer.h, and
Integer.cc
This is a C++
Integer
class that I threw together to make the gmp library work like normal
arithmetic. It lets you play with big integers just like you would with
(int) or (long int). There is also a .tar.gz version available that includes
small Makefile and demo test code.Requires the GMP
library from GNU.

Miracl
Package from Shamus Software Ltd can do multiple precision arithmatic
as well.